On the Convergence of Karhunen-Loeve Series Expansion for a Brownian Particle
W. G. Paff, Goodarz Ahmadi · Journal of Applied Mechanics · 1993
A linear Langevin equation for the velocity of a Brownian particle is considered. The equation of motion is solved and the Karhunen-Loeve expansion for the particle velocity is derived. The mean-square velocity as obtained by the truncated Karhunen-Loeve expansion is compared with the exact solution. It is shown, as the number of terms in the series increases, the result approaches that of the exact solution asymptotically.